Interface Disturbances Caused by Plane Elastic Pulses

In this article the work of Comninou, Dundurs and co-authors on the subject of interface disturbances caused by plane elastic pulses is briefly reviewed. Some paradoxical aspects occurring at high coefficients of friction are pointed out. Some new results are also presented. Introduction If two elastic solids are perfectly bonded, the interface is described as bilateral because it can transmit tensile tractions, and the solids neither separate nor slip unless the bond is broken. If there is no bond, the contact interface between the solids cannot transmit tensile tractions, and the shearing tractions that can be sustained are limited by the available friction. In this case, the solids can easily separate and slip, the boundary conditions contain inequalities, and the interface is described as unilateral. The interaction of elastic waves with a unilateral interface has only recently come under study. In addition to the work of the author and her collaborators [l-11] described in the next sections, the work of R. K. Miller in the modelling of various bonding conditions by generalized friction laws must be mentioned [12-141. The case of viscous loose bonding has been considered by Murty [15,16] and problems connected with moving punches and interface fracture are the subject of ongoing investigation by L. M. Brock [17,18]. Problem Description The first attempt to understand the phenomena involved when cn incident wave strikes a unilateral interface involved a number of idealizations [1,2]. The two solids were half planes held together by applied uniform pressure, the incident wave was plane harmonic and the interface was assumed frictionless. Under these conditions the disturbance caused at the interface is in the form of localized periodic separation zones propagating with constant speed. In this article more attention is paid to the problems in which some of the assumptions mentioned are relaxed: the plane wave may have arbitrary form (plane pulse) and the interface can transmit frictionalforces,which obey Coulomb's law of friction. The coefficients of static and kinetic friction are assumed equal, f. The solids are compressed and sheared at infinity by the uniform applied tractions pm and qa, respectively. The longitudinal and shear wavespeeds, are denofed by cL and c , and bars are used to denote the quantities related to the upper solid. The pulse s T rikes the interface at an angle of incidenceeo measured from the normal to the interface and comes from the side of the lower solid. Before the wave strikes the interface, the latter is in a state of stick. An incident wave of sufficient amplitude causes a disturbance in the form of 2 and separation zones propagating with velocity v = co/sinOo (1) where c is the speed of the incident wave. :wo casgs: Depending on the magnitude of v we distinguish Case I. v is supersonic with respect to both solids,(v>c v> c ). None of the reflected or refracted waves becomes a surface wave. The solutionsLAan beLobtained algebraically 1135